Line the bottom of a 9 by 13-inch baking dish with cookies, breaking them to fill in any gaps along the edges.

Combine the sweetened condensed milk and cream cheese in the bowl of an electric mixer on medium speed. Whisk the heavy cream with the sugar in a large chilled bowl until soft peaks form; set aside. In another mixing bowl, whisk the pudding mix and milk until thoroughly combined. Pour the pudding mixture into the mixing bowl with the cream cheese mixture. Mix until combined. Fold the whipped cream into the pudding mixture.

Pour half of the pudding mixture over the graham crackers, spreading to cover. Top with another layer of graham crackers. Spread the remaining pudding mixture evenly over the crackers. Top with a final layer of graham crackers.

Place chocolate in a medium heatproof bowl. Heat the cream in a small saucepan over medium heat and bring to a simmer. Pour the hot cream over the chocolate and let stand for 5 minutes. Stir in the butter and vanilla until smooth. Pour the ganache over the top graham cracker layer and spread evenly. Cover and refrigerate for at least 4 hours up to overnight before serving.